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A013668 Decimal expansion of zeta(10). 13
1, 0, 0, 0, 9, 9, 4, 5, 7, 5, 1, 2, 7, 8, 1, 8, 0, 8, 5, 3, 3, 7, 1, 4, 5, 9, 5, 8, 9, 0, 0, 3, 1, 9, 0, 1, 7, 0, 0, 6, 0, 1, 9, 5, 3, 1, 5, 6, 4, 4, 7, 7, 5, 1, 7, 2, 5, 7, 7, 8, 8, 9, 9, 4, 6, 3, 6, 2, 9, 1, 4, 6, 5, 1, 5, 1, 9, 1, 2, 9, 5, 4, 3, 9, 7, 0, 4, 1, 9, 6, 8, 6, 1, 0, 3, 8, 5, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.

LINKS

Table of n, a(n) for n=1..99.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

FORMULA

Equals Pi^10/93555.

zeta(10) = 4/3*2^10/(2^10 - 1)*( Sum_{n even} n^2*p(n)/(n^2 - 1)^11 ), where p(n) = 3*n^10 + 55*n^8 + 198*n^6 + 198*n^4 + 55*n^2 + 3 is a row polynomial of A091043. - Peter Bala, Dec 05 2013

zeta(10) = Sum_{n >= 1} (A010052(n)/n^5) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^5 ). - Mikael Aaltonen, Feb 20 2015

zeta(10) = Product_{k>=1} 1/(1 - 1/prime(k)^10). - Vaclav Kotesovec, May 02 2020

From Wolfdieter Lang, Sep 16 2020: (Start)

zeta(10) = (1/9!)*Integral_{0..infinity} x^9/(exp(x) - 1). See Abramowitz-Stegun, 23.2.7., for s=10, p. 807. The value of the integral is (128/33)*Pi^10 = (3.6324091...)*10^5.

zeta(10) = (4/1448685)*Integral_{0..infinity} x^9/(exp(x) + 1). See Abramowitz-Stegun, 23.2.8., for s=10, p. 807. The value of the integral is (511/132)*Pi^10 = (3.625314565...)*10^5. (End)

EXAMPLE

1.0009945751278180853371459589003190170060195315644775172577889946362914...

MATHEMATICA

RealDigits[Zeta[10], 10, 100][[1]] (* Vincenzo Librandi, Feb 15 2015 *)

PROG

(PARI) zeta(10) \\ Michel Marcus, Feb 20 2015

CROSSREFS

Cf. A013662, A013664, A013666, A013670.

Sequence in context: A336044 A019893 A117023 * A143302 A202540 A218708

Adjacent sequences:  A013665 A013666 A013667 * A013669 A013670 A013671

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 1 03:32 EST 2021. Contains 341732 sequences. (Running on oeis4.)